Re #28: My bad. I was combining two different systems.
However, this is not correct, either. They system has more flexibility that it appears here:
But American male descendants, which do have to be in the direct line, no. As I mentioned, the Roman numerals are only used beginning with III, and never (correctly) with II; the second of the same name remains 'Jr.'
John James Doe
John James Doe, Jr.
John James Doe III
John James Doe IV
Of course there may be some families who aren't aware of traditional usage, or just choose differently;
A couple of sites that I've found shows that there is, indeed, more flexibility than the above indicates, including the fact that the descendants need not be directly related as father/son // mother/daughter.
However, with regular people, the use of II and Jr can sometimes be confusing. There is nothing set in stone about how these two name suffixes should be used, but there is a common usage. That common usage is to use Jr when the child is being named directly after his father and to use II when the child is to have the name of an earlier male relative, such as a grandfather, uncle, great-uncle, great-grandfather, etc.
The Jr suffix has some other unofficial rules associated with it. One of these is that calling a man Sr is only to be done after he has passed, and also only when his Jr offspring has married. It is also usually expected that a father still is alive if a child is called Jr. If the child is born posthumously, and the mother wants to name him after the father, he should be called II.